In this letter, we study the design of three-dimensional (3D)-printed ceramics exhibiting anisotropic dielectric permittivities at microwave frequencies for dielectric resonator antenna (DRA) applications. The anisotropy is engineered by using periodic structures made up of subwavelength asymmetric unit cells filled with zirconia and air. Ceramic samples with uniaxial anisotropy are designed, 3D-printed, and measured. Birefringence up to 8 is achieved by controlling the volume fill rate of the unit cell. Besides, a single-fed circularly polarised (CP) DRA that relies on a 3-D-printed uniaxial anisotropic ceramic is proposed in the 2.45 GHz ISM band. Its simulated and measured reflection coefficient, axial ratio, and realised gain patterns are in good agreement, thus demonstrating the possibility of exploiting 3-D-printed anisotropic ceramics for DRA applications.